Organization:
Mechanical and Aerospace Engineering (MAE)

Series

RELIEF: Research & Experimentation for Local & International Emergency First Responders

Description

The mission of the Mechanical and Aerospace Engineering department is to provide defense-relevant, advanced education and research programs to meet Naval unique needs, and increase the warfighting effectiveness of the U.S. Naval Forces, DoD and allied armed forces.

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https://nps.edu/web/mae

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Publication Search Results

Now showing 1 - 10 of 106

Pseudospectral Methods for Optimal Motion Planning of Differentially Flat Systems
(IEEE, 2004-08-01) Ross, I. Michael; Fahroo, Fariba; Modeling, Virtual Environments, and Simulation Institute (MOVES); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Naval Postgraduate School (U.S.); IEEE; Applied Mathematics
This note presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization. We show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to Fliess implicit state variable representation of dynamical systems. The optimal motion planning problem for differentially flat systems is equivalent to a classic Bolza problem of the calculus of variations. In this note, we exploit the notion that derivatives of flat outputs given in terms of Lagrange polynomials at Legendre'Gauss'Lobatto points can be quickly computed using pseudospectral differentiation matrices. Additionally, the Legendre pseudospectral method approximates integrals by Gauss-type quadrature rules. The application of this method to the two-dimensional crane model reveals how differential flatness may be readily exploited.
Convergence of Pseudospectral Discretization of Optimal Control Problems, IEEE (40th; 2001; Orlando, Florida)
(IEEE, 2001-12-01) Ross, Michael I.; Fahroo, Fariba; Modeling, Virtual Environments, and Simulation Institute (MOVES); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Naval Postgraduate School (U.S.); IEEE; Applied Mathematics
A generic nonlinear optimal control problem with a Bolza cost functional is discretized by a Legendre pseudospectral method. According to the covector mapping theorem, the Karush-Kuhn-Tucker multipliers of the discrete problem map linearly to the spectrally discretized covectors of the Bolza problem. Using this result, it is shown that the nonlinear programming problem converges to the continuous Bolza problem at a spectral rate assuming regularity of appropriate functions.
RELIEF Overview
(Monterey, California: Naval Postgraduate School., 2013-09) Institute for Joint Warfare Analysis (IJWA); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Research & Experimentation for Local & International Emergency First-Responders (RELIEF); Naval Postgraduate School
RELIEF provides an environment that fuses interactive community building and knowledge sharing activities with concept-based socio-technological experimentation. Since 2009, RELIEF has brought humanitarian practitioners, technology developers, federal civilians, and active-duty military personnel together for hands on collaboration. The multi-institutional field setting provides a semi-structured learning environment promoting collaboration and relationship building across an increasingly diverse response network.
RELIEF 10-03 After Action Report
(Monterey, California: Naval Postgraduate School., 2010-07-29) Crowley, John; Institute for Joint Warfare Analysis (IJWA); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Research & Experimentation for Local & International Emergency First-Responders (RELIEF); Naval Postgraduate School
The RELIEF 10-03 experiments was the first pause in operations for several of the key free-and-open-source software players in the Haiti response, as well as the first chance many had to work on issues discovered in the field, especially as it relates to the interoperation of their applications with large organizations like the DoD. The attendees included Sahana, OpenStreetMap, Walking Papers, GeoCommons, Synergy Strike Force, and the ESRI. Also attending were Dr. John Gage (Kleiner Perkins and former CTO of Sun Microsystems) and Dr. Linton Wells (Force Transformation Chair, National Defense University and former CIO of the DoD).
RELIEF Newsletter / February 2013 / Issue 6
(Monterey, California: Naval Postgraduate School., 2013-02) Institute for Joint Warfare Analysis (IJWA); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Research & Experimentation for Local & International Emergency First-Responders (RELIEF); Naval Postgraduate School
Second Look at Approximating Differential Inclusions
(2001-02) Fahroo, Fariba; Ross, I., Michael; Modeling, Virtual Environments, and Simulation Institute (MOVES); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Applied Mathematics
In many direct methods for numerically solving optimal control problems, a collocation technique is used. What distinguishes numerous direct collocation schemes is the discretization of the time history and the way the state equations are satisfied at various discrete points. In one of the earliest schemes, cubic splines were used as the interpolating polynomials over the time segments. The state differential equations were imposed at the midpoints by way of a Hermiteﾃ__Simpson implicit integration method. Generalizations of these collocation schemes were employed by Herman and Conway and Conway and Larson in the form of higher-order Gaussﾃ__Lobatto and by Enright and Conway in the form of Rungeﾃ__Kutta-type quadrature rules. The use of higher-order integration rules facilitates a larger step size that results in a smaller number of discretization nodes or optimization variables. Because the efficiency and even convergence of nonlinear programming (NLP)problems improves for a problem of smaller size, finding ways to accurately and ef ficiently discretize optimal control problems is of great interest in this area of research.
Research and Experimentation for Local & International Emergency First- Responders, RELIEF 11-01
(Monterey, California: Naval Postgraduate School., 2010-11-30) Crowley, John; Wells, Linton II; Institute for Joint Warfare Analysis (IJWA); Sharing To Accelerate Research - Transformative Innovation for Development and Emergency Support (STAR-TIDES); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Research & Experimentation for Local & International Emergency First-Responders (RELIEF); Naval Postgraduate School
Research & Experimentation for Local & International Emergency First-Responders (RELIEF) 12-2 Quick Look Report
(Monterey, California: Naval Postgraduate School., 2012-02) Institute for Joint Warfare Analysis (IJWA); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Research & Experimentation for Local & International Emergency First-Responders (RELIEF); Naval Postgraduate School
Naval Postgraduate School RELIEF 12-2 Quick Look Report, Camp Roberts, CA, 27 February - 2 March 2012
Costate Estimation by a Legendre Pseudospectral Method
(Naval Postgraduate School (U.S.), 2001-03-01) Fahroo, Fariba; Ross, I. Michael; Modeling, Virtual Environments, and Simulation Institute (MOVES); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Naval Postgraduate School (U.S.); Department of Aeronautics and Astronautics; Mathematics
We present a Legendre pseudospectral method for directly estimating the costate of the Bolza problem encountered in optimal control theory. The method is based on calculating the state and control variables at the Legendre'Gauss'Lobatto (LGL) points. An Nth degree Lagrange polynomial approximation of these variables allows a conversion of the optimal control problem into a standard nonlinear programming (NLP) problem with the state and control values at the LGL points as optimization parameters. By applying the Karush'Kuhn'Tucker (KKT) theorem to the NLP problem, we show that the KKT multipliers satisfy a discrete analog of the costate dynamics including the transversality conditions. Indeed, we prove that the costates at the LGL points are equal to the KKT multipliers divided by the LGL weights. Hence, the direct solution by this method also automatically yields the costate by way of the Lagrange multipliers that can be extracted from an NLP solver. One important advantage of this technique is that it allows a very simple way to check the optimality of the direct solution. Numerical examples are included to demonstrate the method.
RELIEF Research & Experimentation for Local & International Emergency First-Responders Quick Look Report 12-1 Experimentation: 2-4 November 2011
(Monterey, California: Naval Postgraduate School., 2011-11) Institute for Joint Warfare Analysis (IJWA); Mechanical and Aerospace Engineering (MAE); Graduate School of Engineering and Applied Science (GSEAS); Research & Experimentation for Local & International Emergency First-Responders (RELIEF); Naval Postgraduate School
Naval Postgraduate School RELIEF 12-1 Quick Look Report, Camp Roberts, CA, 2-4 November 2011